EQUILLIBRIUM

1. EQUILLIBRIUM BY GP CAPT NC CHATTOPADHYAY

2. MEANING • Latin aequilībrium,  equivalent to aequi- equi-  + lībr ( a ) balance + -ium –ium • -ium:   a suffix found on nouns borrowed from Latin, especially derivatives of verb • Synonyms  equipoise, steadiness, stability.

3. DEFINITION • Condition in which the net force / and moment acting on a particle is zero. A body in equilibrium experiences no acceleration and, unless disturbed by an outside force /moment, will remain in equilibrium indefinitely.

4. AFTER A LOT OF STUDIES…… EXAMPLE OF EQOUILLIBRIUM

5. TYPES • A stable equilibrium is one in which small, externally induced displacements from that state produce forces that tend to oppose the displacement and return the body to equilibrium • An unstable equilibrium is one in which the least departures produce forces tending to increase the displacement. • IN NEUTRAL EQUILLIBRIUM A BODY IF DISTURBED CHANGES IT’S POSITION AND THEN STEADY. EVERY TIME A NEW POSITION IS ADOPTED • A BALL IN A CUP is in stable equilibrium • brick lying on the Floor is in NEUTRAL equilibrium • a ball ON AN INVERTED CURVED SURFACE is in unstable equilibriuM

6. EXAMPLES

7. REAL TIME SITUATIONS • BODY IS IN MOTION N, τ, V’ ? • BODY IS IN ROTATION N, τ, V’ ? • COMBINED ACTION OF MOTION AND ROTATION • BODY IS AT REST N, τ, V ALL ZERO

8. CONDITIONS • MOTION- ∑F = 0 • ROTATION- ∑M = 0 • COMBINED ACTION - ∑F = 0, ∑M = 0 • REST - ∑F = 0, ∑M = 0

9. CONDITIONS ..CONTD…. • As applied to a rigid body, the necessary and sufficient conditions become: “A rigid body is in mechanical equilibrium when the sum of all forces on all particles of the system is zero, and also the sum of all Moments on all particles of the system is zero. “ A rigid body in mechanical equilibrium is undergoing neither linear nor rotational acceleration; however it could be translating or rotating at a constant velocity.

10. COMPLEX BODY COMPLEX STRUCTURES POSE DIFFICULTY IN ANALYSIS

11. SOLUTION ? • FREE BODY CONCEPT • FREE BODY IS AN ISOLATED BODY SEPARATED FROM THE COMPLEX PARTS REPRESENTING ALL FORCES INCLUDING REACTIONS AND MOMENTS IT EXPERIENCES • IT HELPS IN SOLVING UNKNOWN QUANTITIES USING THE CONCPT OF EQUILLIBRIUM

12. FREE BODY • A free body diagram is a pictorial representation often used by physicists and engineers to analyze the forces acting on a body of interest. • A free body diagram shows all forces of all types acting on this body. Drawing such a diagram can aid in solving for the unknown forces or the equations of motion of the body. Creating a free body diagram can make it easier to understand the forces, and torques or moments, in relation to one another and suggest the proper concepts to apply in order to find the solution to a problem. • The diagrams are also used as a conceptual device to help identify the internal forces—for example, shear forces and bending moments in beams—which are developed within structures.[

13. EXAMPLE

14. EXAMPLE • A simple free body diagram, shown above, of a block on a ramp illustrates this. • All external supports and structures have been replaced by the forces they generate. These include: • mg: the product of the mass of the block and the constant of gravitation acceleration: its weight. • N: the normal force of the ramp. • Ff: the friction force of the ramp. • The force vectors show direction and point of application and are labeled with their magnitude. • It contains a coordinate system that can be used when describing the vectors.

15. LAWS ON EQUILLIBRIUM • LAMI’S THEOREM • CONVERSE OF TRINGLE LAW OF FORCES • CONVERSE OF POLYGON LAW OF FORCES

16. PROOF • LAMI’S THEOREM……… CLASSWORK

17. BRAIN SCRATCHERS………. OSMANY HALL

18. DAY BEGINS WITH NUMERICALS